Certified Programs and Proofs: Second International by Greg Morrisett (auth.), Chris Hawblitzel, Dale Miller (eds.)

By Greg Morrisett (auth.), Chris Hawblitzel, Dale Miller (eds.)

This booklet constitutes the refereed complaints of the second one overseas convention on qualified courses and Proofs, CPP 2012, held in Kyoto, Japan, in December 2012. The 18 revised commonplace papers awarded have been rigorously reviewed and chosen from 37 submissions. They care for these themes in laptop technology and arithmetic within which certification through formal ideas is crucial.

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Succs are defined by trees. [] returns an empty list when a searched-for key in succs does not exist. [x] is a list with one element x. 30 J. Zhao and S. Zdancewic Module Type ALGDOM. Parameter sdom: f →l →set l. Definition dom f l1 := l1 {+} sdom f l1. Axiom entry_sound: forall f e, entry f = Some e →sdom f e = {}. Axiom successors_sound: forall f l1 l2, In l1 (succs f)[l2] →sdom f l1 {<=} dom f l2. Axiom complete: forall f l1 l2, wf f →f |= l1 >> l2 →l1 ‘In‘ (sdom f l2). End ALGDOM. Module AlgDom_Properties(AD: ALGDOM).

On a CFG, we use G |= l1 →∗ l2 to denote a path ρ from l1 to l2 , and l ∈ ρ to denote that l is in the path ρ. By wf f, we require that a well-formed function must contain an entry point that cannot be reached from other blocks, all terminators can only branch to blocks within f , and that all labels in f are unique. In this paper, we consider only well-formed functions to streamline the presentation. edu/~ jianzhou/Vellvm/dominance Mechanized Verification of Computing Dominators Types typ : : = Constants cnst : : = Values val : : = Blocks b :: = Functions f :: = int Int r | cnst l φ c tmn fun {b} Instructions insn : : = Phi Nodes φ :: = Commands c :: = Terminators tmn : : = Non-φs φˆ : : = 29 φ | c | tmn j r = phi typ [valj , lj ] r := val1 bop val2 br l | br val l1 l2 | ret typ val c | tmn Fig.

At each recursive step, find next finds the next available node that is the unvisited node in the Fr scs of the latest node l of the stack. If the next available node exists, the DFS pushes the node with its successors to the stack, and makes the node to be visited. find next pops all nodes in front of l , and gives them PO numbers. If find next fails to find available nodes, the DFS stops. We can see that the straightforward algorithm is not a structural recursion. To implement the algorithm in Coq, we must show that it terminates.

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